Two-Lines: A Valid Alternative to the Invalid Testing of U-Shaped Relationships with Quadratic Regressions

37 Pages Posted: 22 Aug 2017 Last revised: 24 Mar 2018

Uri Simonsohn

University of Pennsylvania - The Wharton School

Date Written: March 21, 2018

Abstract

Many psychological theories predict u-shaped relationships: the effect of x is positive for low values of x, but negative for high values, or vice-versa. Despite implying merely a change of sign, hypotheses about u-shapes are tested almost exclusively via quadratic regressions. The unnecessary and arbitrary quadratic assumption can lead to a 100% false-positive rate, e.g., concluding y=log(x) is u-shaped. Estimating two regression lines, one for low and one high values of x, allows testing for a sign change without functional form assumptions. To set the breakpoint between the lines, I introduce the Robin Hood algorithm. It delivers higher power to detect u-shapes than all breakpoint alternatives considered. The paper includes simulations and re-analyses of published results.

The app: http://webstimate.org/twolines

Keywords: regression, interactoin, quadratic, u-shape, specification error

Suggested Citation

Simonsohn, Uri, Two-Lines: A Valid Alternative to the Invalid Testing of U-Shaped Relationships with Quadratic Regressions (March 21, 2018). Available at SSRN: https://ssrn.com/abstract=3021690 or http://dx.doi.org/10.2139/ssrn.3021690

Uri Simonsohn (Contact Author)

University of Pennsylvania - The Wharton School ( email )

3730 Walnut Street
JMHH 500
Philadelphia, PA 19104-6365
United States

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